| Euclides - 1826 - 226 pages
...be taken greater than p). It is 5. evident that ^* > - f , and £ < i. QED PROPOSITION IX. THEOREM. **Magnitudes which have the same ratio to the same magnitude,...magnitude has the same ratio are equal to one another.** the same ratio« to c, but they have: therefore • 8.5. Again, let c have the same ratio to A and... | |
| James Ryan - Algebra - 1826 - 430 pages
...quotient ; and therefore the ratio of C to B is greater than the ratio of C i& AQED PROP. IX. TIIEOR. **Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio, are equal to one another.** DEMONSTRATION. 1 . Let A and B have the same ratio to C, it is to be proved that A is equal to B. Because... | |
| Euclid - 1826 - 234 pages
...Def.?. 5. evident that -* > -, and ? < £. QED ppmn PROPOSITION IX. THEOREM. Magnitudes which hate **the same ratio to the same magnitude, are equal to...magnitude has the same ratio are equal to one another.** For let each of the magnitudes A, B, have the same ratio to c : then is A equal to B. 129 the same... | |
| Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...ratio to A than it has to A+B [def. 7. 5.). Therefore, &e. QE JL». PROP. IX. THEOR. Magnitudes whieh **have the same ratio to the same magnitude are equal to one another ; and those to** whieh the same magnitude has the same ratio are equal to one another. If A. : C ". B : C, A=B. For,... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...magnitudes, &c. QED PROP. IX. THEOR. Magnitudes which have the same ratio to the same mag- See N. nitude **are equal to one another : and those to which the...magnitude has the same ratio are equal to one another.** Let A, B have each of them the same ratio to C: A shall be equal to B. For, if they are not equal,... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...A, but not greater than m (A + B), C : A is greater than C : A + B. PROPOSITION IX. THEOREM. (486) **Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another.** I,et A, B have each of them the same ratio to C : A is equal toB. For, if they are not equal, one of... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...or a greater ratio to В than it has to A. (See also 9. Cor. 3.) Therefore, &c. Cor. 1. (Eue. v. 9.) **Magnitudes which have the same ratio to the same magnitude are equal** tu one another : as likewise those to which the same magnitude has the same ratio. Cor. 2. A ratio... | |
| Euclid - 1835 - 540 pages
...Wherefore, " of unequal magnitudes," &c. QED 0 B K A C GB LKHD b 7. def. 5. PROP. IX. THEOR. D See N. **Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another.** Let A, B, have each of them the same ratio to C ; then will A be equal to B : For, if they are not... | |
| Mathematics - 1835 - 684 pages
...a greater ratio to В than it has to .\. (See also У. Cor. 3.) Therefore, &c. Cor. I. (Euc.v. 9.) **Magnitudes which have the same ratio to the same magnitude are equal to one another** : as likewise those to which the same magnitude has the same ratio. Cor. 2. A ratio which is compounded... | |
| Robert Simson - Trigonometry - 1835 - 544 pages
...has to AB. Wherefore, " of unequal magnitudes," &c. QED C B HD b7. def. 5. PROP. IX. THEOR. D See N **Magnitudes which have the same ratio to the same magnitude are equal to one** anotlier ; and those to which the same magnitude has the same ratio are equal to one another. Let A,... | |
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